It is possible. Java3D does not detect collision detection for you so you will have to come up with your own method of checking for a collision.
The way of doing this is calculating a bounding box(or supplying one) for each object and then iterating over all of the objects to see if there are any intersections between the bounding boxes. It's a fairly simple algorithm that any game programming or 3d math programming book will cover.
You can also use bounding spheres if the object is spherical or you don't need precision. A sphere intersection check is a bit cheaper than a bounding box collision check. Both are relatively cheap though.
If you are going to have number objects, it would be wise to look into further optimizing the search space by using data structures such as binary space partitions or octrees.